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Displaying similar documents to “Gradient regularity for minimizers of functionals under p - q subquadratic growth”

Existence and boundedness of minimizers of a class of integral functionals

A. Mercaldo (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider a class of integral functionals whose integrand satisfies growth conditions of the type f ( x , η , ξ ) a ( x ) | ξ | p ( 1 + | η | ) α - b 1 ( x ) | η | β 1 - g 1 ( x ) , f ( x , η , 0 ) b 2 ( x ) | η | β 2 + g 2 ( x ) , where 0 α < p , 1 β 1 < p , 0 β 2 < p , α + β i p , a x , b i x , g i x ( i = 1 , 2 ) are nonnegative functions satisfying suitable summability assumptions. We prove the existence and boundedness of minimizers of such a functional in the class of functions belonging to the weighted Sobolev space W 1 , p a , which assume a boundary datum u 0 W 1 , p a L Ω .

Partial Hölder continuity results for solutions of non linear non variational elliptic systems with limit controlled growth

Luisa Fattorusso, Giovanna Idone (2002)

Bollettino dell'Unione Matematica Italiana

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Let Ω be a bounded open subset of R n , n > 4 , of class C 2 . Let u H 2 Ω a solution of elliptic non linear non variational system a x , u , D u , H u = b x , u , D u where a x , u , μ , ξ and b x , u , μ are vectors in R N , N 1 , measurable in x , continuous in u , μ , ξ and u , μ respectively. Here, we demonstrate that if b x , u , μ has limit controlled growth, if a x , u , μ , ξ is of class C 1 in ξ and satisfies the Campanato condition A and, together with a ξ , certain continuity assumptions, then the vector D u is partially Hölder continuous for every exponent α < 1 - n p .

One-dimensional symmetry for solutions of quasilinear equations in R 2

Alberto Farina (2003)

Bollettino dell'Unione Matematica Italiana

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In this paper we consider two-dimensional quasilinear equations of the form div a u u + f u = 0 and study the properties of the solutions u with bounded and non-vanishing gradient. Under a weak assumption involving the growth of the argument of u (notice that arg u is a well-defined real function since u > 0 on R 2 ) we prove that u is one-dimensional, i.e., u = u ν x for some unit vector ν . As a consequence of our result we obtain that any solution u having one positive derivative is one-dimensional. This result provides...

Hölder continuity results for a class of functionals with non-standard growth

Michela Eleuteri (2004)

Bollettino dell'Unione Matematica Italiana

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We prove regularity results for real valued minimizers of the integral functional f x , u , D u under non-standard growth conditions of p x -type, i.e. L - 1 z p x f x , s , z L 1 + z p x under sharp assumptions on the continuous function p x > 1 .